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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
130.2.a.a 130.a 1.a $1$ $1.038$ \(\Q\) None \(-1\) \(-2\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-4q^{7}+\cdots\)
130.2.a.b 130.a 1.a $1$ $1.038$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
130.2.a.c 130.a 1.a $1$ $1.038$ \(\Q\) None \(1\) \(2\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots\)
130.2.b.a 130.b 5.b $6$ $1.038$ 6.0.3534400.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(\beta _{3}-\beta _{4})q^{3}-q^{4}+(\beta _{3}+\beta _{5})q^{5}+\cdots\)
130.2.c.a 130.c 65.d $4$ $1.038$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-4\) \(0\) \(3\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{3})q^{5}+\beta _{2}q^{6}+\cdots\)
130.2.c.b 130.c 65.d $4$ $1.038$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(4\) \(0\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta _{2}q^{3}+q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
130.2.d.a 130.d 13.b $2$ $1.038$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2q^{3}-q^{4}+iq^{5}+2iq^{6}+\cdots\)
130.2.e.a 130.e 13.c $2$ $1.038$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+3\zeta_{6}q^{7}+\cdots\)
130.2.e.b 130.e 13.c $2$ $1.038$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
130.2.e.c 130.e 13.c $4$ $1.038$ \(\Q(\sqrt{-3}, \sqrt{10})\) None \(-2\) \(0\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
130.2.e.d 130.e 13.c $4$ $1.038$ \(\Q(\zeta_{12})\) None \(2\) \(-2\) \(4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
130.2.g.a 130.g 65.k $2$ $1.038$ \(\Q(\sqrt{-1}) \) None \(-2\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-q^{2}+(-2-2i)q^{3}+q^{4}+(-2-i)q^{5}+\cdots\)
130.2.g.b 130.g 65.k $2$ $1.038$ \(\Q(\sqrt{-1}) \) None \(-2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-q^{2}+(1+i)q^{3}+q^{4}+(-1+2i)q^{5}+\cdots\)
130.2.g.c 130.g 65.k $2$ $1.038$ \(\Q(\sqrt{-1}) \) None \(2\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+(-1-i)q^{3}+q^{4}+(1-2i)q^{5}+\cdots\)
130.2.g.d 130.g 65.k $4$ $1.038$ \(\Q(i, \sqrt{11})\) None \(-4\) \(2\) \(6\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+q^{4}+\cdots\)
130.2.g.e 130.g 65.k $4$ $1.038$ \(\Q(\zeta_{12})\) None \(4\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
130.2.j.a 130.j 65.f $2$ $1.038$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(-2\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-iq^{2}+(-2+2i)q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
130.2.j.b 130.j 65.f $2$ $1.038$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+iq^{2}+(-1+i)q^{3}-q^{4}+(-2+i)q^{5}+\cdots\)
130.2.j.c 130.j 65.f $2$ $1.038$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-iq^{2}+(1-i)q^{3}-q^{4}+(2-i)q^{5}+\cdots\)
130.2.j.d 130.j 65.f $4$ $1.038$ \(\Q(i, \sqrt{11})\) None \(0\) \(2\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}-q^{4}+\cdots\)
130.2.j.e 130.j 65.f $4$ $1.038$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{3}q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
130.2.l.a 130.l 13.e $4$ $1.038$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(1+\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots\)
130.2.l.b 130.l 13.e $8$ $1.038$ 8.0.22581504.2 None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(\beta _{2}-\beta _{4}-\beta _{7})q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
130.2.m.a 130.m 65.l $8$ $1.038$ 8.0.\(\cdots\).1 None \(-4\) \(0\) \(3\) \(5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{3})q^{2}-\beta _{2}q^{3}-\beta _{3}q^{4}-\beta _{7}q^{5}+\cdots\)
130.2.m.b 130.m 65.l $8$ $1.038$ 8.0.\(\cdots\).1 None \(4\) \(0\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{3}+\cdots)q^{4}+\cdots\)
130.2.n.a 130.n 65.n $12$ $1.038$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}-\beta _{5}q^{3}+\beta _{8}q^{4}+(-\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots\)
130.2.p.a 130.p 65.t $12$ $1.038$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{6}q^{2}+(\beta _{5}+\beta _{7}+\beta _{8}+\beta _{11})q^{3}+\cdots\)
130.2.p.b 130.p 65.t $16$ $1.038$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{4})q^{3}+(1+\beta _{8}+\cdots)q^{4}+\cdots\)
130.2.s.a 130.s 65.o $12$ $1.038$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}-\beta _{11})q^{3}+(-1+\cdots)q^{4}+\cdots\)
130.2.s.b 130.s 65.o $16$ $1.038$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(8\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\beta _{8})q^{2}+(\beta _{2}-\beta _{11})q^{3}+\beta _{8}q^{4}+\cdots\)
130.3.f.a 130.f 65.g $14$ $3.542$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-14\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{4})q^{2}+\beta _{1}q^{3}+2\beta _{4}q^{4}+\cdots\)
130.3.f.b 130.f 65.g $14$ $3.542$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(14\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{4})q^{2}-\beta _{1}q^{3}+2\beta _{4}q^{4}+\beta _{10}q^{5}+\cdots\)
130.3.h.a 130.h 65.h $2$ $3.542$ \(\Q(\sqrt{-1}) \) None \(-2\) \(-4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{2}+(-2+2i)q^{3}-2iq^{4}+\cdots\)
130.3.h.b 130.h 65.h $2$ $3.542$ \(\Q(\sqrt{-1}) \) None \(2\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{2}+(-2+2i)q^{3}-2iq^{4}+\cdots\)
130.3.h.c 130.h 65.h $12$ $3.542$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(4\) \(8\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{3})q^{2}+\beta _{2}q^{3}-2\beta _{3}q^{4}+\cdots\)
130.3.h.d 130.h 65.h $12$ $3.542$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(4\) \(-8\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\beta _{3})q^{2}+\beta _{2}q^{3}-2\beta _{3}q^{4}+(-1+\cdots)q^{5}+\cdots\)
130.3.i.a 130.i 5.c $12$ $3.542$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(8\) \(-12\) \(-16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{2})q^{2}+(1+\beta _{2}+\beta _{4})q^{3}+\cdots\)
130.3.i.b 130.i 5.c $12$ $3.542$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\beta _{3})q^{2}+\beta _{2}q^{3}-2\beta _{3}q^{4}+(1+\cdots)q^{5}+\cdots\)
130.3.k.a 130.k 13.d $12$ $3.542$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{4})q^{2}-\beta _{2}q^{3}+2\beta _{4}q^{4}+\cdots\)
130.3.k.b 130.k 13.d $12$ $3.542$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(12\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{6})q^{2}+\beta _{3}q^{3}+2\beta _{6}q^{4}-\beta _{7}q^{5}+\cdots\)
130.3.o.a 130.o 13.f $16$ $3.542$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-8\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\beta _{2}-\beta _{11})q^{2}+(-\beta _{3}+\beta _{5}+\beta _{6}+\cdots)q^{3}+\cdots\)
130.3.o.b 130.o 13.f $16$ $3.542$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(8\) \(0\) \(0\) \(32\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\beta _{3}-\beta _{6}-\beta _{7})q^{2}+(\beta _{7}+\beta _{10}+\cdots)q^{3}+\cdots\)
130.3.q.a 130.q 65.q $8$ $3.542$ 8.0.5802782976.1 None \(-4\) \(2\) \(24\) \(-14\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\beta _{1}-\beta _{2}+\beta _{5})q^{2}+(-\beta _{2}-\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)
130.3.q.b 130.q 65.q $16$ $3.542$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-8\) \(-2\) \(-28\) \(18\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\beta _{6}-\beta _{9}+\beta _{13})q^{2}+\beta _{15}q^{3}+\cdots\)
130.3.q.c 130.q 65.q $32$ $3.542$ None \(16\) \(0\) \(12\) \(-4\) $\mathrm{SU}(2)[C_{12}]$
130.3.r.a 130.r 65.r $28$ $3.542$ None \(-14\) \(0\) \(8\) \(4\) $\mathrm{SU}(2)[C_{12}]$
130.3.r.b 130.r 65.r $28$ $3.542$ None \(14\) \(0\) \(-8\) \(-4\) $\mathrm{SU}(2)[C_{12}]$
130.3.t.a 130.t 65.s $28$ $3.542$ None \(-14\) \(0\) \(-2\) \(12\) $\mathrm{SU}(2)[C_{12}]$
130.3.t.b 130.t 65.s $28$ $3.542$ None \(14\) \(0\) \(4\) \(-12\) $\mathrm{SU}(2)[C_{12}]$
130.4.a.a 130.a 1.a $1$ $7.670$ \(\Q\) None \(-2\) \(-2\) \(5\) \(8\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+4q^{4}+5q^{5}+4q^{6}+\cdots\)
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